Net Positive Suction Head ( NPSH ) is extremely important to the operation of a centrifugal pump. Factors that affect NPSH are atmospheric pressure, suction line friction loss, elevation, fluid temperature and SG.
To calculate NPSHA: NPSHA = (PAF – PVF) / SG ± Z -SHF;
where:
- PAF = atmospheric pressure, feet—at sea level is 34 feet of water. Therefore, if the supply tank is a vented or open-air tank at sea level, the atmosphere will apply 34 feet of pressure to the fluid surface. When the pump casing is filled with liquid and then activated, pressure at the eye of the impeller drops. Atmospheric pressure, being greater than this value, pushes liquid into the pump suction. The pump does not suck fluid; fluid is pushed into the pump by the atmosphere.
- PVF = vapor pressure, in feet—the amount of head required to maintain fluid in a liquid state. This value (for water) can be found in Table 1.
- SG = specific gravity of fluid.
- SHF = suction head friction losses, calculated as shown previously.
- Z¼elevation, or the liquid level above or below the pump centerline, in feet. If the supply tank is mounted on the same level as the pump, the elevation is the number of feet the fluid is above the centerline. Therefore, if the tank is 9 feet tall and when full has 8 feet 9 inches of liquid, then 8 feet can be added to the NPSHA equation as long as the tank is not going to be drained (centerline of the pump is 9 inches). If there is a desire to have the ability to drain the tank, this value should not be added to the equation. If the fluid level is below the pump centerline, this distance must be subtracted from the equation (the lowest possible liquid surface level should be used when calculating).
Table 1. Properties of Water
Temperature | Vapor pressure | ||
F | C | psi | ft |
40 | 4.4 | 0.12 | 0.28 |
50 | 10 | 0.18 | 0.41 |
60 | 15.6 | 0.26 | 0.59 |
70 | 21.1 | 0.36 | 0.82 |
80 | 26.7 | 0.51 | 1.17 |
90 | 32.2 | 0.70 | 1.61 |
100 | 37.8 | 0.95 | 2.19 |
110 | 43.3 | 1.28 | 2.94 |
120 | 48.9 | 1.69 | 3.91 |
130 | 54.4 | 2.22 | 5.15 |
140 | 60 | 2.89 | 6.68 |
150 | 65.6 | 3.72 | 8.56 |
160 | 71.1 | 4.74 | 10.95 |
170 | 76.7 | 5.99 | 13.84 |
180 | 82.2 | 7.51 | 17.35 |
190 | 87.8 | 9.34 | 21.55 |
200 | 93.3 | 11.50 | 26.65 |
212 | 100 | 14.70 | 33.96 |
F = 1.0×9/5×C +32; |
To continue the previous example, the suction line will be 8 inches; flow rate, 1000 gpm; fluid temperature, 180F; location is sea level; tank is open vented; liquid level above pump centerline is 8 feet; and there is not a desire to drain the tank. The 8-inch-diameter. suction line has one elbow, one branched tee, and one butterfly valve and is 30 feet long:
Atmospheric pressure = 34 feet of water
Vapor pressure = ? feet
SG = 1.92
Suction line friction losses previously calculated = 2.23 feet
Elevation = 8 feet
To determine vapor pressure of the fluid, refer to the properties of water in Table 1.
Water-based drilling mud in 180F will require 17.9 feet of head to maintain fluid in a liquid state:
NPSHA = (PAF – PVF) / SG ± Z -SHF;
Therefore
NPSHA = （34 – 17.35 )/1.92 + 8 – 2.23 = 14.44
Review the centrifugal pump curve in Figure 1 to determine NPSHR for the pump at the operating point (shown by the arrow).
In Figure 1, NPSHR at the operating point is slightly less than halfway between 7 and 13 feet and would therefore equal 10 feet NPSHR. Because NPSHA is 14.44 and NPSHR is 10 feet, the pump will still have 4.44 feet of positive head that will prevent fluid from cavitating. If NPSHA were less than or equal to NPSHR, the pump would cavitate and damage would occur.
Fluid temperature/vapor pressure is the most common factor overlooked during pump sizing. However, in this example it was the most significant factor in determining NPSHA.
Note that NPSH values are used only to determine whether adequate head will be maintained on the suction side of the pump to prevent cavitation. It does not, however, have any bearing on TDH required by the system.
System Head Requirement (SHR) Worksheet
A worksheet is a useful tool for sizing a centrifugal pump. Following a worksheet will simplify the sizing process and allows the user to calculate TDH required. An SHR Worksheet problem is given in Exercise 2 at the end of the chapter.
Affinity Laws
If there is a known operating point and a different operating point is required, the following algebraic formulas can be used to accurately predict what changes should be made to alter flow or head and what the resulting horsepower requirements will be. A pump’s performance can be altered by changing speed or by changing impeller diameter.
Note: Speed formulas are very reliable. Impeller diameter formulas are
accurate only for small variations in diameter.
Friction Loss Formulas
Friction loss 1 / Friction loss 2 = (gpm 1)²/(gpm 2)²
If a particular operating point and elevation of a system are known, it is possible to calculate a new operating point by using the following friction loss formulas. Assume that a system exists that has 20 feet of elevation and the pump is transferring water at 500 gpm and the pressure gauge reads 50 psi at the pump discharge. What head is required to produce 1000 gpm?
- First convert psi to feet: Head = 50 psi × 2:31⁄1.0SG; Head = 115 feet
- Subtract lift of 20 feet, since this is a constant: 115 feet head – 20 feet elevation = 95 feet of system friction loss at 500 gpm.
- Utilize friction loss formulas to determine the new head required to produce 1000 gpm in this system: Friction loss 1 / Friction loss 2 = (gpm 1)²/(gpm 2)²; or X/95 = 1000²/500²= 380 feet;
- Add back lift: 380+20=400.
It would therefore be necessary to size a pump for 1000 gpm at 400 feet to obtain the desired flow rate of 1000 gpm in the existing system. Note: It may be more economical to alter system discharge piping to reduce system friction losses than to pay power costs to produce 400 feet of head.
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